I'm thinking if lower level plants such as algae are more sensitive to this form of O.
Okay, so... add ozone, it decomposes through a radical route, so does peroxide. Why doesn't dosing peroxide/ozone directly to a tank help?
This is all terrible pseudo-science at best, especially the cosmetic example you give. Its fine to hypothesize but the next step is to test your hypothesis, or at least give me a reference to something peer reviewed... You could setup two small tanks, introduce plants and algae to both at the same levels dose one with peroxide, don't dose peroxide for the other, take pictures as the weeks go on. But until someone does this experiment it senseless to talk about radicals beating back algae.
A non-pseudoscience prediction is that radicals will readily oxidize any organic matter in your water column, such as tannins, organic matter and the chelating agent holding your iron in the proper oxidation state... you can find this in any water treatment handbook.